Question: Solve for $x$ and $y$ using elimination. ${-3x+3y = 3}$ ${6x-2y = 26}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ ${-6x+6y = 6}$ $6x-2y = 26$ Add the top and bottom equations together. $4y = 32$ $\dfrac{4y}{{4}} = \dfrac{32}{{4}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x+3y = 3}\thinspace$ to find $x$ ${-3x + 3}{(8)}{= 3}$ $-3x+24 = 3$ $-3x+24{-24} = 3{-24}$ $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ You can also plug ${y = 8}$ into $\thinspace {6x-2y = 26}\thinspace$ and get the same answer for $x$ : ${6x - 2}{(8)}{= 26}$ ${x = 7}$